The nonhomogeneous minimal surface equation involving a measure
Copyright policy )The nonhomogeneous minimal surface equation involving a measure
We find existence of a minimum in BV for the variational problem associated with \(\text{div } A(Du)+ \mu= 0\), where \(A\) is a mean curvature type operator and \(\mu\) a nonnegative measure satisfying a suitable growth condition. We then show a local \(L^ \infty\) estimate for the minimum. A similar local \(L^ \infty\) estimate is shown for sub- solutions that are Sobolev rather than BV.
local bound solution, minimal surface equation, Minimal surfaces and optimization, variational solution, 58E12, Nonlinear elliptic equations, 35D99, nonlinear elliptic partial differential equations, 49Q05, 35J60
local bound solution, minimal surface equation, Minimal surfaces and optimization, variational solution, 58E12, Nonlinear elliptic equations, 35D99, nonlinear elliptic partial differential equations, 49Q05, 35J60
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